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Write and equation in slope intercept form through (5,2) and parallel to the given line y=-5x+3

Sagot :

For Parallelism condition, the slope of the two(2) lines are equal.

i.e:

[tex]m_1=m_2[/tex]

From the given equation of the line:

[tex]y=-5x+3[/tex]

Comparing this with the standard straight line equation: y= mx + c, where m represents the slope, we have:

[tex]m=-5[/tex]

Since the lines are parallel; the new slope is also equal to -5.

Thus,

[tex]\begin{gathered} m_1=m_2 \\ m_2=-5 \end{gathered}[/tex]

Now that we know the slope and a point (5, -2), we can use the slope formula:

[tex]\begin{gathered} m=\frac{y-y_1}{x-x_1} \\ m=-5 \\ \text{from the point (5,2);} \\ x_1=5,y_1=2 \end{gathered}[/tex]

Thus, we have:

[tex]\begin{gathered} -5=\frac{y-2}{x-5} \\ \text{cross}-\text{multiply;} \\ y-2=-5(x-5) \\ y-2=-5x+25 \\ y=-5x+25+2 \\ y=-5x+27 \end{gathered}[/tex]

Hence, the equation in slope-intercept form is:

[tex]y=-5x+27[/tex]

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