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QuestionFind the line equation through points (1,5)(1,5) and (−6,−3)(-6,-3). y=y=

Studdy Solution

STEP 1

Assumptions1. The line passes through the points (1,5) and (-6,-3) . The equation of a line can be written in the form y=mx+by = mx + b where m is the slope and b is the y-intercept.

STEP 2

First, we need to find the slope of the line. The slope (m) can be calculated using the formulam=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}

STEP 3

Now, plug in the given values for the coordinates of the two points to calculate the slope.
m=−3−5−6−1m = \frac{-3 -5}{-6 -1}

STEP 4

Calculate the slope.
m=−8−7=87m = \frac{-8}{-7} = \frac{8}{7}

STEP 5

Now that we have the slope, we can find the y-intercept (b) using the formulab=y−mxb = y - mxWe can use the coordinates of either of the two given points. Let's use the point (1,5).

STEP 6

Plug in the values for y, m, and x to calculate the y-intercept.
b=5−8×1b =5 - \frac{8}{} \times1

STEP 7

Calculate the y-intercept.
b=5−7=357−7=277b =5 - \frac{}{7} = \frac{35}{7} - \frac{}{7} = \frac{27}{7}

STEP 8

Now that we have the slope and the y-intercept, we can write the equation of the line.
y=mx+by = mx + b

STEP 9

Plug in the values for m and b to write the equation of the line.
y=87x+277y = \frac{8}{7}x + \frac{27}{7}So, the equation of the line that passes through the points (,5) and (-6,-3) is y=87x+277y = \frac{8}{7}x + \frac{27}{7}.

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