marleneicamacho
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Write an equation in slope-intercept form for the line with [tex]y[/tex]-intercept -3 and slope [tex]-\frac{3}{2}[/tex].

[tex]y = -\frac{3}{2}x - 3[/tex]

Sagot :

GinnyAnswer
To find the equation of a line in slope-intercept form given a slope and a y-intercept, you can use the formula for slope-intercept form, which is:

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

where:
- [tex]\( m \)[/tex] is the slope
- [tex]\( b \)[/tex] is the y-intercept

In this case, you are given a slope ([tex]\( m \)[/tex]) of [tex]\(-\frac{3}{2}\)[/tex] and a y-intercept ([tex]\( b \)[/tex]) of [tex]\(-3\)[/tex].

Substitute the given values into the slope-intercept form equation:

[tex]\[ y = \left( -\frac{3}{2} \right)x + (-3) \][/tex]

This can be written more clearly as:

[tex]\[ y = -\frac{3}{2}x - 3 \][/tex]

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

[tex]\[ y = -1.5x + -3 \][/tex]
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