Answer :
To find the equation of a line with a given slope that passes through a specific point, we use the point-slope form of the equation of a line. The point-slope form is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\( m \)[/tex] is the slope, and [tex]\( (x_1, y_1) \)[/tex] is a point on the line.
Given:
- The slope [tex]\( m = 3 \)[/tex]
- The point [tex]\((-3, -5)\)[/tex]
Substitute these values into the point-slope form equation:
[tex]\[ y - (-5) = 3(x - (-3)) \][/tex]
Simplify the equation by performing the arithmetic operations:
[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 into slope-intercept form [tex]\( y = mx + b \)[/tex], isolate [tex]\( y \)[/tex] by subtracting 5 from both sides:
[tex]\[ y = 3x + 9 - 5 \][/tex]
[tex]\[ y = 3x + 4 \][/tex]
So, the equation of the line is:
[tex]\[ y = 3x + 4 \][/tex]
Therefore, 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 a point on the line.
Given:
- The slope [tex]\( m = 3 \)[/tex]
- The point [tex]\((-3, -5)\)[/tex]
Substitute these values into the point-slope form equation:
[tex]\[ y - (-5) = 3(x - (-3)) \][/tex]
Simplify the equation by performing the arithmetic operations:
[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 into slope-intercept form [tex]\( y = mx + b \)[/tex], isolate [tex]\( y \)[/tex] by subtracting 5 from both sides:
[tex]\[ y = 3x + 9 - 5 \][/tex]
[tex]\[ y = 3x + 4 \][/tex]
So, the equation of the line is:
[tex]\[ y = 3x + 4 \][/tex]
Therefore, the correct answer is:
A. [tex]\( y = 3x + 4 \)[/tex]
