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What is the equation of the line that has a slope of 3 and goes through the point [tex]\((-3, -5)\)[/tex]?

A. [tex]\( y = 3x + 4 \)[/tex]

B. [tex]\( y = 3x - 14 \)[/tex]

C. [tex]\( y = 3x - 4 \)[/tex]

D. [tex]\( y = 3x + 12 \)[/tex]

Sagot :

GinnyAnswer
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]
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