A line in the xy-plane passes through the origin and has a slope of 1/7. Which of the following points lies on the line? A) (0, 7) B) (1, 7) C) (7, 7) D) (14, 2)

Identify Equation: Step 1: Identify the equation of the line using the slope and the fact that it passes through the origin. The slope-intercept form of a line is y = mx + b. Since the slope (m) is 1/7 and it passes through the origin (b=0), the equation of the line is y = (1/7)x. Check Point A: Step 2: Substitute the x and y values of each point into the equation y = (1/7)x to check if they satisfy the equation. For point A (0, 7): y = (1/7)*0 = 0 Check: 7 ≠ 0 Check Point B: Step 3: Check point B (1, 7): y = (1/7)*1 = 1/7 Check: 7 ≠ 1/7 Check Point C: Step 4: Check point C (7, 7): y = (1/7)*7 = 1 Check: 7 ≠ 1 Check Point D: Step 5: Check point D (14, 2): y = (1/7)*14 = 2 Check: 2 = 2

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A line in the $xy$ -plane passes through the origin and has a slope of $\frac{1}{7}$ . Which of the following points lies on the line? $\newline$ A) $(0, 7)$ $\newline$ B) $(1, 7)$ $\newline$ C) $(7, 7)$ $\newline$ D) $(14, 2)$

View step-by-step help

Home

Math Problems

Grade 7

Find a missing coordinate using slope

Full solution

Q. A line in the

xy

-plane passes through the origin and has a slope of

\frac{1}{7}

. Which of the following points lies on the line?

\newline

(0, 7)

\newline

(1, 7)

\newline

(7, 7)

\newline

(14, 2)

Identify Equation: Step $1$ : Identify the equation of the line using the slope and the fact that it passes through the origin. The slope-intercept form of a line is $y = mx + b$ . Since the slope $(m)$ is $\frac{1}{7}$ and it passes through the origin $(b=0)$ , the equation of the line is $y = \left(\frac{1}{7}\right)x$ .
Check Point A: Step $2$ : Substitute the $x$ and $y$ values of each point into the equation $y = \frac{1}{7}x$ to check if they satisfy the equation. $\newline$ For point A $(0, 7)$ : $\newline$ $y = \frac{1}{7}\cdot0 = 0$ $\newline$ Check: $7 \neq 0$
Check Point B: Step $3$ : Check point B $(1, 7)$ : $\newline$ $y = (\frac{1}{7})\cdot1 = \frac{1}{7}$ $\newline$ Check: $7 \neq \frac{1}{7}$
Check Point C: Step $4$ : Check point C $(7, 7)$ : $\newline$ $y = (\frac{1}{7})*7 = 1$ $\newline$ Check: $7 \neq 1$
Check Point D: Step $5$ : Check point D $(14, 2)$ : $\newline$ $y = (\frac{1}{7})\cdot14 = 2$ $\newline$ Check: $2 = 2$