Answer :
To find the equation of a line that has a given slope and goes through a specified point, we can use the point-slope form of the equation of a line. The point-slope form is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\(m\)[/tex] is the slope, and [tex]\((x_1, y_1)\)[/tex] is the point that the line passes through.
Given the slope [tex]\(m = 3\)[/tex] and the point [tex]\((-3, -5)\)[/tex], we can substitute these values into the point-slope form:
[tex]\[ y - (-5) = 3(x - (-3)) \][/tex]
Simplify the equation:
[tex]\[ y + 5 = 3(x + 3) \][/tex]
Distribute the 3 on the right-hand side:
[tex]\[ y + 5 = 3x + 9 \][/tex]
To get the equation in slope-intercept form ( [tex]\(y = mx + b\)[/tex] ), we need to isolate [tex]\(y\)[/tex] on one side of the equation. Subtract 5 from both sides:
[tex]\[ y = 3x + 9 - 5 \][/tex]
Simplify:
[tex]\[ y = 3x + 4 \][/tex]
Therefore, the equation of the line is:
[tex]\[ y = 3x + 4 \][/tex]
So, the correct answer is:
A. [tex]\(y = 3x + 4\)[/tex]
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\(m\)[/tex] is the slope, and [tex]\((x_1, y_1)\)[/tex] is the point that the line passes through.
Given the slope [tex]\(m = 3\)[/tex] and the point [tex]\((-3, -5)\)[/tex], we can substitute these values into the point-slope form:
[tex]\[ y - (-5) = 3(x - (-3)) \][/tex]
Simplify the equation:
[tex]\[ y + 5 = 3(x + 3) \][/tex]
Distribute the 3 on the right-hand side:
[tex]\[ y + 5 = 3x + 9 \][/tex]
To get the equation in slope-intercept form ( [tex]\(y = mx + b\)[/tex] ), we need to isolate [tex]\(y\)[/tex] on one side of the equation. Subtract 5 from both sides:
[tex]\[ y = 3x + 9 - 5 \][/tex]
Simplify:
[tex]\[ y = 3x + 4 \][/tex]
Therefore, the equation of the line is:
[tex]\[ y = 3x + 4 \][/tex]
So, the correct answer is:
A. [tex]\(y = 3x + 4\)[/tex]
