Final answer:
To write the equation of a line in slope-intercept form, we need to find the slope and the y-intercept. The equation of the line through the points (4, -2) and (0, 5) in slope-intercept form is y = (-7 / 4)x + 5.
Step-by-step explanation:
To write the equation of a line in slope-intercept form, we need to find the slope and the y-intercept.
- First, find the slope. The slope is given by the formula: m = (y2 - y1) / (x2 - x1). Using the points (4, -2) and (0, 5), we have: m = (-2 - 5) / (4 - 0) = -7 / 4.
- Next, find the y-intercept. The y-intercept is the point where the line crosses the y-axis. We can use one of the given points, (4, -2), to find the y-intercept. Substitute the coordinates into the slope-intercept form: -2 = (-7 / 4) * 4 + b. Solve for b to find the y-intercept. b = -2 + (7 / 4) * 4 = -2 + 7 = 5.
- Finally, substitute the values of the slope (m = -7 / 4) and y-intercept (b = 5) into the slope-intercept form: y = mx + b. Therefore, the equation of the line is y = (-7 / 4)x + 5 in slope-intercept form.