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4. Which equation describes the line with slope 5 that contains the point [tex]\((-2, 4)\)[/tex]?

A. [tex]\(y = 5x - 22\)[/tex]
B. [tex]\(y = 5x - 2\)[/tex]
C. [tex]\(y = 5x + 4\)[/tex]
D. [tex]\(y = 5x + 14\)[/tex]

Sagot :

GinnyAnsweridn
To determine the equation of a line given a slope and a point the line passes through, 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 a point on the line.

Given:
- Slope [tex]\( m = 5 \)[/tex]
- Point [tex]\((-2, 4)\)[/tex]

Plugging these values into the point-slope form:

[tex]\[ y - 4 = 5(x - (-2)) \][/tex]

Simplify the equation:

[tex]\[ y - 4 = 5(x + 2) \][/tex]

Distribute the slope on the right-hand side:

[tex]\[ y - 4 = 5x + 10 \][/tex]

Now, isolate [tex]\( y \)[/tex] to convert the equation into the slope-intercept form [tex]\( y = mx + b \)[/tex]:

[tex]\[ y = 5x + 10 + 4 \][/tex]

Combine the constant terms:

[tex]\[ y = 5x + 14 \][/tex]

Therefore, the correct equation of the line is:

[tex]\[ \boxed{y = 5x + 14} \][/tex]

This corresponds to choice [tex]\( d \)[/tex].
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