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Math  /  Algebra

Question\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|} \hline & & & & & & & & & & \\ \hline \end{tabular}
What is the equation of a line containing the points (7,6)(7,6) and (4,3)(4,3). Submit your answer in slope-intercept form. equation: \qquad

Studdy Solution

STEP 1

1. We are given two points: (7,6) (7, 6) and (4,3) (4, 3) .
2. We need to find the equation of the line passing through these points.
3. The equation should be in slope-intercept form, which is y=mx+b y = mx + b .

STEP 2

1. Calculate the slope m m of the line.
2. Use the slope and one point to find the y-intercept b b .
3. Write the equation in slope-intercept form.

STEP 3

Calculate the slope m m of the line using the formula:
m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Substitute the given points (x1,y1)=(7,6) (x_1, y_1) = (7, 6) and (x2,y2)=(4,3) (x_2, y_2) = (4, 3) :
m=3−64−7 m = \frac{3 - 6}{4 - 7} m=−3−3 m = \frac{-3}{-3} m=1 m = 1

STEP 4

Use the slope m=1 m = 1 and one of the points, say (4,3) (4, 3) , to find the y-intercept b b using the equation y=mx+b y = mx + b .
Substitute m=1 m = 1 , x=4 x = 4 , and y=3 y = 3 :
3=1⋅4+b 3 = 1 \cdot 4 + b 3=4+b 3 = 4 + b
Solve for b b :
b=3−4 b = 3 - 4 b=−1 b = -1

STEP 5

Write the equation in slope-intercept form y=mx+b y = mx + b .
Substitute m=1 m = 1 and b=−1 b = -1 :
y=1x−1 y = 1x - 1
Simplify the equation:
y=x−1 y = x - 1
The equation of the line in slope-intercept form is:
y=x−1 \boxed{y = x - 1}

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