Find the equation of the straight line passing for points (2, −1) and (1, 1). (ii) Simplify (d)/(d x)(x2+2 x)

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a) Find the equation of the straight line joining the points (2, 7) and (1, 1). Step 1: Calculate the slope (m) of the line using the formula m = (y₂ − y₁)/(x₂ − x₁). Given points (x₁, y₁) = (2, 7) and (x₂, y₂) = (1, 1). m = (1 − 7)/(1 − 2); m = (−6)/(−1); m = 6; Step 2: Use the point-slope form of the equation of a line, y − y₁ = m(x − x₁), with one of the points, for example (1, 1), and the calculated slope m=6. y − 1 = 6(x − 1); Step 3: Simplify the equation to the slope-intercept form y = mx + c. y − 1 = 6x − 6; y = 6x − 6 + 1; y = 6x − 5; The equation of the straight line is y = 6x − 5. b) Simplify 1/2(A − 1/3). Step 1: Distribute 1/2 to each term inside the parenthesis. 1/2 (A − 1/3) = 1/2 · A − 1/2 · 1/3 Step 2: Perform the multiplication. = A/2 − 1/6 The simplified expression is A/2 − 1/6.

Find the equation of the straight line passing for points (2, -1) and (1, 1). (ii) Simplify (d)/(d x)(x2+2 x)

Answers

Step-by-step solution

Part a· 3 steps

Calculate the slope ( $m$ ) of the line using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

Use the point-slope form of the equation of a line, $y - y_1 = m(x - x_1)$ , with one of the points, for example $(1, 1)$ , and the calculated slope $m=6$ .

Simplify the equation to the slope-intercept form $y = mx + c$ .

Part b· 2 steps
$\mathbf{\frac{A}{2} - \frac{1}{6}}$

Distribute $\frac{1}{2}$ to each term inside the parenthesis.

Perform the multiplication.

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