Question

Write the slope-intercept form of the equation of the line that passes through the two points. Graph the line. Label the points where the line crosses the axes. \((2,0),(-4,-3)\)

Short answer

The slope-intercept form of the line passing through the points (2,0),(-4,-3) is \(y = 0.5x - 1\). The line crosses the y-axis at (0,-1) and the x-axis at (2,0).

Step-by-step solution

Find the Slope m

The slope between the two points (2,0) and (-4,-3) is given by \(m=(y_2-y_1)/(x_2-x_1)\), so \(m=(-3-0)/(-4-2) = -3/-6 = 0.5\).

Find the y-intercept b

For determining \(b\), apply the slope and any of the two points in the following standard slope-intercept form: \(y = mx + b\). Using point (2,0) and \(m=0.5\) gives: \(0 = 0.5*2 + b\), which leads to \(b=-1\).

Write the Slope-Intercept Form of the Equation

Now that the slope \(m=0.5\) and the y-intercept \(b=-1\) have been determined, substitute these values into the equation \(y = mx + b\), to obtain the final solution: \(y = 0.5x - 1\).

Graph the Line

To graph the line, first plot the y-intercept (0,-1). Then from this point, apply the slope (rise over run) to find two more points. The rise is 0.5, which means to go up by 0.5 and the run is 1 means go to the right by 1. This would give another point (1,-0.5). Repeat this process once more to have at least three points to draw a line precisely. Finally, label the points of intersection with the axes, which are (0,-1) and (2,0).