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Math  /  Algebra

QuestionWhich equation is a point slope form equation for line ABA B ? y+1=32(x−4)y+1=\frac{3}{2}(x-4) y+1=−23(x−4)y+1=-\frac{2}{3}(x-4) y+1=23(x−4)y+1=\frac{2}{3}(x-4) y+1=−32(x−4)y+1=-\frac{3}{2}(x-4)

Studdy Solution

STEP 1

What is this asking? Find the equation of the line that goes through points A(4,−1) A(4, -1) and B(−2,3) B(-2, 3) using the point-slope form. Watch out! Don't mix up the slope calculation!
Remember, it's rise over run, not the other way around.

STEP 2

1. Calculate the slope
2. Use point-slope form

STEP 3

To find the slope m m of the line through points A(4,−1) A(4, -1) and B(−2,3) B(-2, 3) , we use the formula for slope:
m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}Plug in the coordinates of points A A and B B :
m=3−(−1)−2−4m = \frac{3 - (-1)}{-2 - 4}

STEP 4

Simplify the expression:
m=3+1−6=4−6=−23m = \frac{3 + 1}{-6} = \frac{4}{-6} = -\frac{2}{3}So, the **slope** of the line is **−23-\frac{2}{3}**.

STEP 5

The point-slope form of a line is given by:
y−y1=m(x−x1)y - y_1 = m(x - x_1)We can use either point A(4,−1) A(4, -1) or point B(−2,3) B(-2, 3) .
Let's use point A(4,−1) A(4, -1) .

STEP 6

Substitute the slope m=−23 m = -\frac{2}{3} and the coordinates of point A(4,−1) A(4, -1) into the point-slope form:
y−(−1)=−23(x−4)y - (-1) = -\frac{2}{3}(x - 4)

STEP 7

Simplify the equation:
y+1=−23(x−4)y + 1 = -\frac{2}{3}(x - 4)This is the equation of the line in point-slope form.

STEP 8

The equation of the line in point-slope form is y+1=−23(x−4) y + 1 = -\frac{2}{3}(x - 4) .

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