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Complete the equation of the line through $(2,1)$ and $(5,-8)$

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Write a linear equation from two points

Full solution

Q. Complete the equation of the line through

(2,1)

and

(5,-8)

Calculate slope: Calculate the slope $m$ of the line using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ with the given points $(2,1)$ and $(5,-8)$ . $\newline$ $m = \frac{-8 - 1}{5 - 2}$ $\newline$ $m = \frac{-9}{3}$ $\newline$ $m = -3$
Find y-intercept: Use one of the points and the slope to find the y-intercept $b$ of the line. Let's use the point $(2,1)$ . Substitute $x = 2$ , $y = 1$ , and $m = -3$ into the equation $y = mx + b$ . $\newline$ $1 = -3(2) + b$ $\newline$ $1 = -6 + b$ $\newline$ $b = 1 + 6$ $\newline$ $b = 7$
Write equation: Write the equation of the line in slope-intercept form $y = mx + b$ using the calculated slope and y-intercept. $\newline$ $y = -3x + 7$

More problems from Write a linear equation from two points

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(0, 4)

satisfy the equation

y = x

?

\newline

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

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Question

Rewrite the following equation in slope-intercept form.

\newline

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y

-intercept of the line

14x - 16y = -10

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

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q

\frac{-2}{3}

r

is perpendicular to

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. What is the slope of line

r

\newline

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

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\_\_\_\_\_

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

\newline

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

Posted 2 months 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 2 months 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 3 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 3 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 2 months ago