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A line passes through the point [tex]\((-3, 5)\)[/tex] and has a slope of -3.

Write an equation in slope-intercept form for this line.

Sagot :

GinnyAnswer
To derive the equation of the line in slope-intercept form (which is [tex]\( y = mx + b \)[/tex]), we need two pieces of information: the slope [tex]\( m \)[/tex] and the y-intercept [tex]\( b \)[/tex]. We are given:

- A point the line passes through: [tex]\((-3, 5)\)[/tex]
- The slope of the line [tex]\( m = -3 \)[/tex]

Step 1: Substitute the given point and slope into the slope-intercept form equation.

The general equation of the line in slope-intercept form is:
[tex]\[ y = mx + b \][/tex]

Substitute [tex]\( x = -3 \)[/tex], [tex]\( y = 5 \)[/tex], and [tex]\( m = -3 \)[/tex] into the equation:

[tex]\[ 5 = (-3)(-3) + b \][/tex]

Step 2: Solve for the y-intercept [tex]\( b \)[/tex].

[tex]\[ 5 = 9 + b \][/tex]

Subtract 9 from both sides to isolate [tex]\( b \)[/tex]:

[tex]\[ 5 - 9 = b \][/tex]

[tex]\[ b = -4 \][/tex]

Step 3: Substitute the values of [tex]\( m \)[/tex] and [tex]\( b \)[/tex] back into the slope-intercept form equation.

So, the slope [tex]\( m = -3 \)[/tex] and the y-intercept [tex]\( b = -4 \)[/tex]. Plugging these values in, we get:

[tex]\[ y = -3x - 4 \][/tex]

Therefore, the equation of the line in slope-intercept form is:
[tex]\[ y = -3x - 4 \][/tex]
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