marleneicamacho
Answered

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Write an equation in slope-intercept form for the line with slope [tex]\frac{1}{4}[/tex] and [tex]\( y \)[/tex]-intercept [tex]\(-2\)[/tex].

[tex]\[ \boxed{y = \frac{1}{4}x - 2} \][/tex]

Sagot :

GinnyAnswer
To write the equation of a line in slope-intercept form, we use the general formula:

[tex]\[ y = mx + b \][/tex]

where:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept of the line. This is the point where the line crosses the y-axis.

Given the problem:
- The slope [tex]\( m \)[/tex] is [tex]\( \frac{1}{4} \)[/tex].
- The y-intercept [tex]\( b \)[/tex] is [tex]\(-2\)[/tex].

Substitute these values into the slope-intercept form equation:

[tex]\[ y = \frac{1}{4}x + (-2) \][/tex]

or, simplifying the expression:

[tex]\[ y = 0.25x - 2 \][/tex]

Thus, the equation of the line in slope-intercept form is:

[tex]\[ y = 0.25x - 2 \][/tex]
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