Question

Write an equation for the line in point/slope form and slope/intercept form that has the given condition.

4. Slope= 3/2 and passes through the origin


5. X-intercept=4 and Y-intercept=-3

Answer 1

Write an equation for the line in point/slope form and slope/intercept form that has the given condition.

4. Slope = 3/2 and passes through the origin

5. X-intercept=4 and Y-intercept=-3

**Solution:**

4. The slope of the line is $m = \frac{3}{2}$

In the point/slope form we have $y - y_{1} = m(x - x_{1})$

$$y - 0 = \frac{3}{2}(x - 0)$$ $$y = \frac{3}{2}x$$

In the slope/intercept form $y = \frac{3}{2}x + b$

If it passes through $(0,0)$ then $0 = \frac{3}{2} * 0 + b \quad \Rightarrow \quad b = 0$

So in the slope/intercept form we have: $y = \frac{3}{2}x$

Answer: $y = \frac{3}{2}x$

$$y = \frac{3}{2}x$$

5. The slope of the line is $m = \frac{3}{4}$

In the point/slope form we have $y - y_{1} = m(x - x_{1})$

$$y - (-3) = \frac{3}{4}(x + 0)$$ $$y + 3 = \frac{3}{4}x$$

In the slope/intercept form $y = \frac{3}{4}x + b$

If it passes through $(0, -3)$ then $-3 = \frac{3}{4} * 0 + b \quad \Rightarrow \quad b = -3$

So in the slope/intercept form we have: $y = \frac{3}{4}x - 3$

Answer: $y + 3 = \frac{3}{4}x$

$$y = \frac{3}{4}x - 3$$