Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Determine the equation through the lines through the points $(-21,5)$ and $(7,13)$

View step-by-step help

View step-by-step help

Write a linear equation from two points

Full solution

Q. Determine the equation through the lines through the points

(-21,5)

and

(7,13)

Calculate Slope: Given points: $\newline$ $(-21, 5)$ and $\newline$ $(7, 13)$ $\newline$ Find the slope of the line using the points. $\newline$ Slope, $m$ $\newline$ $= \frac{y_2 - y_1}{x_2 - x_1}$ $\newline$ $= \frac{13 - 5}{7 - (-21)}$ $\newline$ $= \frac{8}{28}$ $\newline$ $= \frac{2}{7}$ $\newline$ So, $m = \frac{2}{7}$
Find Y-Intercept: We have: $\newline$ $m: \frac{2}{7}$ $\newline$ Point: $(7, 13)$ $\newline$ Find the value of $b$ , the y-intercept. $\newline$ Substitute $x = 7$ , $y = 13$ , and $m = \frac{2}{7}$ in $y = mx + b$ . $\newline$ $13 = \left(\frac{2}{7}\right)(7) + b$ $\newline$ $13 = 2 + b$ $\newline$ $13 - 2 = b$ $\newline$ $(7, 13)$ $0$ $\newline$ So, $(7, 13)$ $1$
Write Equation: We found: $\newline$ $m: \frac{2}{7}$ $\newline$ $b: 11$ $\newline$ Write the equation of the line in slope-intercept form. $\newline$ Substitute $m = \frac{2}{7}$ and $b = 11$ in $y = mx + b$ . $\newline$ $y = \left(\frac{2}{7}\right)x + 11$ $\newline$ Slope-intercept form: $y = \left(\frac{2}{7}\right)x + 11$

More problems from Write a linear equation from two points

Question

(0, 4)

satisfy the equation

y = x

?

\newline

Choices: [[yes]][[no]]

Posted 2 months ago

Question

Find the slope of the line

y = -4x + \frac{2}{5}

\newline

Write your answer as an integer or as a simplified proper or improper fraction.

Posted 1 month ago

Question

Rewrite the following equation in slope-intercept form.

\newline

y + 8 = -8(x - 10)

\newline

Write your answer using integers, proper fractions, and improper fractions in simplest form.

\newline

Posted 1 month ago

Question

y

-intercept of the line

14x - 16y = -10

\newline

Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.

\newline

Posted 1 month ago

Question

q

\frac{-2}{3}

r

is perpendicular to

q

. What is the slope of line

r

\newline

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

\newline

\_\_\_\_\_

Posted 1 month ago

Question

Find the slope of the line

y + 3 = -\frac{1}{18}(x + 6)

\newline

Write your answer as an integer or as a simplified proper or improper fraction.

Posted 1 month ago

Question

p

has an equation of

y = -8x + 6

q

, which is perpendicular to line

p

, includes the point

(2, -2)

. What is the equation of line

q

?

\newline

Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

\newline

Posted 1 month ago

Question

Is the graph of this equation a horizontal or vertical line?

\newline

x = 7

\newline

\newline

\text{(A)horizontal line}

\newline

\text{(B)vertical line}

Posted 2 months ago

Question

Rewrite the following equation in standard form.

\newline

y = -10x + 7

\newline

Hint: The standard form of a linear equation is

\newline

Ax + By = C

A

B

are not both zero, and

A

B

C

are integers whose GCF is

1

Posted 2 months ago

Question

A line with a slope of

9

passes through the point

(9,9)

. What is its equation in point-slope form?

\newline

Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.

\newline

y - \underline{\hspace{1cm}} = \underline{\hspace{1cm}} (x - \underline{\hspace{1cm}})

Posted 1 month ago