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A linear equation written in standard form is shown.

-4x+5y=10
What is the slope of the line?

-(4)/(5)

(5)/(4)

(4)/(5)

-4

A linear equation written in standard form is shown. $\newline$ $-4 x+5 y=10$ $\newline$ What is the slope of the line? $\newline$ $-\frac{4}{5}$ $\newline$ $\frac{5}{4}$ $\newline$ $\frac{4}{5}$ $\newline$ $-4$

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Equations of horizontal and vertical lines

Full solution

Q. A linear equation written in standard form is shown.

\newline

-4 x+5 y=10

\newline

What is the slope of the line?

\newline

-\frac{4}{5}

\newline

\frac{5}{4}

\newline

\frac{4}{5}

\newline

-4

Convert to slope-intercept form: Convert the standard form equation to slope-intercept form $y = mx + b$ . $\newline$ The standard form of the equation is $-4x + 5y = 10$ . To find the slope, we need to solve for $y$ to get the equation into slope-intercept form.
Isolate y term: Add $4x$ to both sides of the equation to isolate the $y$ term on one side. $\newline$ $-4x + 5y + 4x = 10 + 4x$ $\newline$ This simplifies to: $\newline$ $5y = 4x + 10$
Solve for y: Divide all terms by $5$ to solve for y. $\newline$ $\frac{5y}{5} = \frac{(4x + 10)}{5}$ $\newline$ This simplifies to: $\newline$ $y = \left(\frac{4}{5}\right)x + 2$
Identify the slope: Identify the slope from the slope-intercept form of the equation. $\newline$ The slope-intercept form of the equation is $y = mx + b$ , where $m$ is the slope. From the equation $y = \frac{4}{5}x + 2$ , the slope $m$ is $\frac{4}{5}$ .

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