Straight Lines Quiz: Geometry Test!

The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is given as 5 and the y-intercept is -2. Therefore, the equation of the line is y = 5x - 2.

In the slope-intercept form, y=mx+b, the variable b represents the y-intercept. The y-intercept is the point where the graph of the function intersects the y-axis. It indicates the value of y when x is equal to zero. So, in this case, b represents the initial value or the value of y when x=0.

The point (1,1) is not on the line y = 2x + 1 because when we substitute x = 1 into the equation, we get y = 2(1) + 1 = 3, which is not equal to 1. Therefore, the point (1,1) does not satisfy the equation and is not on the line.

substitute in zero for x and evaluate the right side of the equation

To find the slope between two points, we use the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the first point are (4, -2) and the coordinates of the second point are (-1, 6). Plugging these values into the formula, we get (6 - (-2)) / (-1 - 4), which simplifies to 8 / -5. Therefore, the slope between these two points is -8/5.

The x-value -1 has two y-values 7 and 8.

The equation 2x+3y=18 can be rearranged into slope-intercept form, which is y=mx+b, where m represents the slope and b represents the y-intercept. In this case, the correct answer is y=-(2/3)x+6, which means that the slope is -(2/3) and the y-intercept is 6.

The slope of a linear equation is the coefficient of the variable x. In this case, the coefficient of x is -2, which means that for every unit increase in x, the y-value decreases by 2 units.

The given equation represents two lines in the form of 2x + 4y = 8x + 2y = 6. By simplifying the equation, we can rewrite it as 2x + 4y = 6 and 8x + 2y = 6. The slopes of these lines can be determined by rearranging the equations in slope-intercept form (y = mx + b), where m represents the slope. The first equation can be rewritten as y = -0.5x + 1.5, and the second equation can be rewritten as y = -4x + 3. Comparing the slopes, we can see that they are both different (-0.5 and -4), indicating that the lines are not parallel, perpendicular, or intersecting. Therefore, the correct answer is "Neither".

If two lines have the same slope and different y-intercepts, it means that they are parallel to each other. Parallel lines never intersect, as they maintain a constant distance between them at all points. Therefore, the correct answer is that the lines will never intersect.

To find the y-intercept of a line, we need to set the value of x to 0 and solve for y. In the given equation, when x is 0, we have 2(0) - y = 6, which simplifies to -y = 6. By multiplying both sides of the equation by -1, we get y = -6. Therefore, the y-intercept of the line is -6.

The given equation is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this case, the equation is 2y = -8 + 3x, which can be rewritten as y = (3/2)x - 4. By substituting the x and y values of each point into the equation, we can determine if it satisfies the equation. Only the point (4,2) satisfies the equation, making it the solution.

The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. In this question, the slope is given as 2/3 and the line passes through the point (9, -3). To find the y-intercept, we substitute the values of x and y from the given point into the equation and solve for b. Plugging in x = 9 and y = -3, we get -3 = (2/3)(9) + b. Simplifying this equation gives b = -9. Therefore, the equation of the line is y = 2/3 x - 9.

The formula for slope is rise over run. This means that to calculate the slope, you divide the change in the y-values (rise) by the change in the x-values (run). It represents the steepness or incline of a line on a graph.

The correct answer explains the steps to graphing a linear equation in a clear and logical manner. It starts by solving for y by isolating it, which allows us to identify the slope and y-intercept. Then, we plot the y-intercept on the graph and use the slope to plot another point. Finally, we connect the two points with a line to graph the linear equation. This answer provides a comprehensive and accurate explanation of the process.

The form of a function that is written as ax+by=c is called the standard form. In this form, the coefficients a, b, and c represent the constants in the equation. The variables x and y represent the independent and dependent variables, respectively. The standard form is commonly used in mathematics to represent linear equations and is useful for solving systems of equations and finding the x and y-intercepts.