Studdy AI Logo
Math

QuestionFind the slope-intercept form of the line through the points: 7) (2,5)(2,5) and (0,3)(0,3) 8) (3,3)(3,3) and (0,5)(0,5).

Studdy Solution

STEP 1

Assumptions1. We are given two points for each line. . The slope-intercept form of a line is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.

STEP 2

First, we need to find the slope of the line. The slope is given by the formulam=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}

STEP 3

For the first line (7), plug in the given points into the slope formulam=5−32−0m = \frac{5 -3}{2 -0}

STEP 4

Calculate the slope for the first line (7).
m=22=1m = \frac{2}{2} =1

STEP 5

Now, we need to find the y-intercept of the line. We can use the formulab=y−mxb = y - mx

STEP 6

For the first line (), plug in the slope and one of the given points into the y-intercept formulab=5−1⋅2b =5 -1 \cdot2

STEP 7

Calculate the y-intercept for the first line (7).
b=5−2=3b =5 -2 =3

STEP 8

Now we can write the equation of the first line (7) in slope-intercept formy=mx+by = mx + b

STEP 9

Plug in the slope and y-intercept for the first line (7) into the slope-intercept equationy=x+3y =x +3

STEP 10

For the second line (8), plug in the given points into the slope formulam=3−53−0m = \frac{3 -5}{3 -0}

STEP 11

Calculate the slope for the second line (8).
m=−3m = \frac{-}{3}

STEP 12

For the second line (8), plug in the slope and one of the given points into the y-intercept formulab=−(−2)⋅b = - (-\frac{2}{}) \cdot

STEP 13

Calculate the y-intercept for the second line (8).
b=3−(−2)=5b =3 - (-2) =5

STEP 14

Now we can write the equation of the second line (8) in slope-intercept formy=mx+by = mx + b

STEP 15

Plug in the slope and y-intercept for the second line (8) into the slope-intercept equationy=−23x+5y = -\frac{2}{3}x +5The slope-intercept forms of the lines are7) y=x+3y = x +3 8) y=−23x+5y = -\frac{2}{3}x +5

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord