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Write the equation of a line with a slope of 3 and passing through the point [tex](-5,-7)[/tex].

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GinnyAnsweridn
To write the equation of the line with a given slope and a point it passes through, we will use the point-slope form of the linear equation. The general formula for the point-slope form is:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

where:
- [tex]\( m \)[/tex] is the slope
- [tex]\( (x_1, y_1) \)[/tex] is a point on the line

Given:
- Slope [tex]\( m = 3 \)[/tex]
- Point [tex]\( (x_1, y_1) = (-5, -7) \)[/tex]

Let's substitute these values into the point-slope formula:

[tex]\[ y - (-7) = 3(x - (-5)) \][/tex]

Simplify the equation:

[tex]\[ y + 7 = 3(x + 5) \][/tex]

Next, distribute the slope on the right side:

[tex]\[ y + 7 = 3x + 15 \][/tex]

Now, solve for [tex]\( y \)[/tex] to get the equation in slope-intercept form [tex]\( y = mx + b \)[/tex]:

[tex]\[ y = 3x + 15 - 7 \][/tex]

Simplify the constants on the right-hand side:

[tex]\[ y = 3x + 8 \][/tex]

So, the equation of the line is:

[tex]\[ y = 3x + 8 \][/tex]

In addition to this, we can verify:
- The slope [tex]\( m = 3 \)[/tex]
- The given point [tex]\((-5, -7)\)[/tex]
- The intercept (constant term in the equation [tex]\( y = mx + b \)[/tex]) is [tex]\( 8 \)[/tex].

Thus, the detailed step-by-step solution results in the equation:

[tex]\[ y = 3x + 8 \][/tex]
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