Question

determine the equation of the line for the given information:
two points on the line are (0, 4) and (7, 18). use the points to first determine the slope and y-intercept. then write the
equation of the line.
a. \\( m = 2, y-\text{int} = (0,4), y = 2x + 4 \\)
b. \\( m = -2, y-\text{int} = (0,4), y = -2x + 4 \\)
c. \\( m = -2, y-\text{int} = (4,0), y = -2x + 4 \\)
d. \\( m = 2, y-\text{int} = (0,4), y = 4x + 2 \\)

please select the best answer from the choices provided
\\( \circ \\) a
\\( \circ \\) b
\\( \circ \\) c
\\( \circ \\) d

Explanation:

Step1: Calculate the slope

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using points $(0, 4)$ (where $x_1 = 0, y_1 = 4$) and $(7, 18)$ (where $x_2 = 7, y_2 = 18$), we get $m = \frac{18 - 4}{7 - 0} = \frac{14}{7} = 2$.

Step2: Identify the y - intercept

The y - intercept is the point where $x = 0$. For the point $(0, 4)$, when $x = 0$, $y = 4$, so the y - intercept is $(0, 4)$.

Step3: Write the equation of the line

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Substituting $m = 2$ and $b = 4$, we get $y = 2x + 4$.

Answer:

A. $m = 2$, $y - \text{int}=(0,4)$, $y = 2x + 4$