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$The equation of the line in point-slope form is y-3=(9)/(8)(x+7). (Type an equation. Use integers or fractions for any numbers in the equation.) The equation of the line in general form is ◻=0. (Type an expression using x and y as the variables. Simplify your answer. Use integers or fractions for any numbers in the expression.)$

The equation of the line in point-slope form is $y-3=\frac{9}{8}(x+7)$ . $\newline$ (Type an equation. Use integers or fractions for any numbers in the equation.) $\newline$ The equation of the line in general form is $\square=0$ . $\newline$ (Type an expression using $x$ and $y$ as the variables. Simplify your answer. Use integers or fractions for any numbers in the expression.)

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Find equations of tangent lines using limits

Full solution

Q. The equation of the line in point-slope form is

y-3=\frac{9}{8}(x+7)

.

\newline

(Type an equation. Use integers or fractions for any numbers in the equation.)

\newline

The equation of the line in general form is

\square=0

.

\newline

(Type an expression using

x

and

y

as the variables. Simplify your answer. Use integers or fractions for any numbers in the expression.)

Rephrase Equation: Rephrase the given equation: $y - 3 = \frac{9}{8}(x + 7)$
Distribute Coefficient: Distribute $\frac{9}{8}$ to $x + 7$ : $y - 3 = \frac{9}{8}x + \frac{9}{8} \cdot 7$
Calculate Result: Calculate $(\frac{9}{8}) \cdot 7$ : $y - 3 = \frac{9}{8}x + \frac{63}{8}$
Isolate $y$ : Add $3$ to both sides to isolate $y$ : $y = \frac{9}{8}x + \frac{63}{8} + 3$
Convert to Fraction: Convert $3$ to a fraction with denominator $8$ : $y = \frac{9}{8}x + \frac{63}{8} + \frac{24}{8}$
Combine Fractions: Combine the fractions: $y = \frac{9}{8}x + \frac{87}{8}$
Clear Fraction: Multiply everything by $8$ to clear the fraction: $8y = 9x + 87$
Rearrange General Form: Rearrange to general form: $9x - 8y + 87 = 0$

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