Question

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. x-intercept = -1/2 and y-intercept = 4

Accepted Answer

Recall that the x-intercept is the point where the line crosses the x-axis, so the coordinates are $$\left(-\frac{1}{2}, 0\right)$$, and the y-intercept is where the line crosses the y-axis, so the coordinates are $$(0, 4). $$Calculate the slope $$m of $$the line using the formula for slope between two points $$\left(x_1$, y_1$\right)$$ and $$\left(x_2$, y_2$\right)$$:

$$m = \frac{y_2$ - y_1$}{x_2$ - x_1$}$$

Substitute the intercept points:

$$m = \frac{4 - 0}{0 - \left(-\frac{1}{2}\right)}$$ Write the equation of the line in point-slope form using the slope $$m$$ and one of the intercept points, for example, the y-intercept $$(0, 4)$$:

$$y - y_1$ = m(x - x_1$)$$

which becomes

$$y - 4 = m(x - 0)$$ Simplify the point-slope form equation to get the slope-intercept form $$y = mx + b$$, where $$b is $$the y-intercept:

$$y = mx + 4$$ You now have both forms:  
- Point-slope form: $$y - 4 = m(x - 0)  
- $$Slope-intercept form: $$y = mx + 4$$  
where $$m is $$the slope calculated in step 2.

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. x-intercept = -1/2 and y-intercept = 4

Verified video answer for a similar problem:

Key Concepts

Intercepts of a Line

Slope of a Line

Forms of Linear Equations