Final answer:
To write the equation of a line in slope-intercept form given a point and a slope, substitute the slope and the point's coordinates into the slope-intercept equation and solve for the y-intercept. In this case, the linear equation is y = -3/5x.
Step-by-step explanation:
To find the equation of a line in slope-intercept form, which is y = mx + b, we will use the given slope (−3/5) and point (−5, 3). We plug these values into the slope-intercept form to solve for the y-intercept (b).
- Start with the slope-intercept form: y = mx + b.
- Substitute the slope (m) and the coordinates of the given point into the equation: 3 = (−3/5)(−5) + b.
- Multiply the slope by the x-coordinate: 3 = 3 + b.
- Solve for b: 3 − 3 = b, which simplifies to b = 0.
The linear equation is therefore y = −3/5x.