Certainly! To find the equation of a line passing through the points [tex]\((-5, 2)\)[/tex] and [tex]\((0, 7)\)[/tex], we can follow these steps:
1. Determine the slope ([tex]\(m\)[/tex]):
- The slope [tex]\(m\)[/tex] is calculated using the formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substituting the coordinates [tex]\((x_1, y_1) = (-5, 2)\)[/tex] and [tex]\((x_2, y_2) = (0, 7)\)[/tex], we get:
[tex]\[
m = \frac{7 - 2}{0 - (-5)} = \frac{5}{5} = 1
\][/tex]
2. Find the y-intercept ([tex]\(c\)[/tex]):
- The equation of the line in slope-intercept form is [tex]\(y = mx + c\)[/tex].
- We can use one of the given points to find [tex]\(c\)[/tex]. Let's use the point [tex]\((0, 7)\)[/tex]:
[tex]\[
y = mx + c \implies 7 = (1) \cdot 0 + c \implies c = 7
\][/tex]
3. Write the equation:
- Now we have the slope [tex]\(m = 1\)[/tex] and the y-intercept [tex]\(c = 7\)[/tex].
- The equation of the line is:
[tex]\[
y = 1 x + 7 \implies y = x + 7
\][/tex]
Therefore, the equation that describes the line is [tex]\( y = x + 7 \)[/tex], which corresponds to option (a).
