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The equation $5x+10y = 30$ is graphed in the $xy$ -plane. Which of the statements below is true of its graph?

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Describe the graph of a linear equation

Full solution

Q. The equation

5x+10y = 30

is graphed in the

xy

-plane. Which of the statements below is true of its graph?

Identify Equation Type: Identify the type of the equation. $\newline$ The given equation $5x + 10y = 30$ is a linear equation in two variables $x$ and $y$ .
Rewrite in Slope-Intercept Form: Rewrite the equation in slope-intercept form $y = mx + b$ . $\newline$ To do this, solve for $y$ : $\newline$ $10y = -5x + 30$ $\newline$ $y = \frac{-5}{10}x + \frac{30}{10}$ $\newline$ $y = -\frac{1}{2}x + 3$
Determine Slope and Y-Intercept: Determine the slope and y-intercept from the slope-intercept form. $\newline$ The slope $m$ is $-\frac{1}{2}$ , and the y-intercept $b$ is $3$ .
Interpret Slope and Y-Intercept: Interpret the slope and y-intercept in terms of the graph. $\newline$ The slope of $-\frac{1}{2}$ means that for every unit increase in $x$ , $y$ decreases by $\frac{1}{2}$ unit. The y-intercept of $3$ means that the line crosses the y-axis at the point $(0, 3)$ .
Describe Graph: Describe the graph based on the slope and y-intercept. $\newline$ The graph is a straight line with a slope of $-\frac{1}{2}$ and a y-intercept at $(0, 3)$ . It extends infinitely in both directions on the $xy$ -plane.

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