Question

write the equation of the line in slope intercept form that goes through the points (3, 4) and (0, -5)
y = -5x + 4
y = 3x - 5
y = -3x + 4
y = 2x - 5

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using the points (3, 4) and (0, -5), we have $x_1 = 3, y_1 = 4, x_2 = 0, y_2 = -5$. So $m = \frac{-5 - 4}{0 - 3} = \frac{-9}{-3} = 3$.

Step2: Find the y-intercept (b)

The slope-intercept form is $y = mx + b$. We know the point (0, -5) is the y-intercept (since x=0), so $b = -5$.

Step3: Write the equation

Substitute m = 3 and b = -5 into $y = mx + b$, we get $y = 3x - 5$.

Answer:

B. $y = 3x - 5$