Determine the intercepts of the line. Do not round your answers. y-4=7(x-6) x-intercept: (◻,◻) y-intercept: (◻,◻)

Finding the x-intercept: To find the x-intercept, we set y to 0 and solve for x. y - 4 = 7(x - 6) Substitute y = 0. 0 - 4 = 7(x - 6) -4 = 7x - 42Isolating the term with x: Now, we add 42 to both sides to isolate the term with x. -4 + 42 = 7x - 42 + 42 38 = 7xSolving for x: Next, we divide both sides by 7 to solve for x. 38 / 7 = 7x / 7 x = 38 / 7Finding the y-intercept: To find the y-intercept, we set x to 0 and solve for y. y - 4 = 7(x - 6) Substitute x = 0. y - 4 = 7(0 - 6) y - 4 = -42Solving for y: Now, we add 4 to both sides to solve for y. y - 4 + 4 = -42 + 4 y = -38

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Math Problems

Algebra 1

Standard form: find x- and y-intercepts

Full solution

Q. Determine the intercepts of the line.

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Do not round your answers.

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y-4=7(x-6)

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x-intercept:

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(\square,\square)

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y-intercept:

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(\square,\square)

Finding the x-intercept: To find the x-intercept, we set $y$ to $0$ and solve for $x$ .
$y - 4 = 7(x - 6)$
Substitute $y = 0$ .
$0 - 4 = 7(x - 6)$
$-4 = 7x - 42$
Isolating the term with x: Now, we add $42$ to both sides to isolate the term with $x$ . $\newline$ $-4 + 42 = 7x - 42 + 42$ $\newline$ $38 = 7x$
Solving for x: Next, we divide both sides by $7$ to solve for x. $\newline$ $\frac{38}{7} = \frac{7x}{7}$ $\newline$ $x = \frac{38}{7}$
Finding the y-intercept: To find the y-intercept, we set $x$ to $0$ and solve for $y$ . $\newline$ $y - 4 = 7(x - 6)$ $\newline$ Substitute $x = 0$ . $\newline$ $y - 4 = 7(0 - 6)$ $\newline$ $y - 4 = -42$
Solving for y: Now, we add $4$ to both sides to solve for $y$ . $\newline$ $y - 4 + 4 = -42 + 4$ $\newline$ $y = -38$