-y%3D-4x%2B2-slope-intercept-form.jpeg "(-2 5) Y=-4x+2 Slope Intercept Form")
Finding the Equation of a Line in Slope-Intercept Form
We are given a point (-2, 5) and a slope of -4, and we need to find the equation of the line in slope-intercept form (y = mx + c).
1. Understand Slope-Intercept Form:
The slope-intercept form of a linear equation is y = mx + c, where:
- m represents the slope of the line.
- c represents the y-intercept (the point where the line crosses the y-axis).
2. Substitute the Given Slope:
We know the slope (m) is -4. Substitute this into the slope-intercept form:
y = -4x + c
3. Use the Given Point to Find the Y-Intercept:
We have a point (-2, 5) that lies on the line. This means that when x = -2, y = 5. Substitute these values into the equation:
5 = -4(-2) + c
4. Solve for the Y-Intercept (c):
Simplify the equation:
5 = 8 + c
Subtract 8 from both sides:
-3 = c
5. Write the Final Equation:
We now know the slope (m = -4) and the y-intercept (c = -3). Substitute these values into the slope-intercept form:
y = -4x - 3
Therefore, the equation of the line in slope-intercept form is y = -4x - 3.