Answer:
y = 3x - 8
Step-by-step explanation:
All the options are written in slope-intercept ( [tex]y = mx + b[/tex]) form. So, what we can do with the given information is write the equation in point-slope form first, then convert it to slope-intercept form.
1) First, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] to find the point-slope equation of the line. Substitute [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] for real values.
Since [tex]m[/tex] represents the slope, substitute 3 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line intersects, substitute the x and y values of (5,7) into the appropriate places in the formula as well. This gives the following equation of the line in point-slope form:
[tex]y-7 = 3(x-5)[/tex]
2) Now, isolate y in the above equation to find its slope-intercept form.
[tex]y-7=3(x-5)\\y-7 = 3x-15\\y = 3x -8[/tex]
Thus, the answer would be the third option as it matches the result we received.
