Questions: Determine which form of a line the given equation is in. Then, determine the slope, the x-intercept, and the y-intercept. Select the answer choice that correctly identifies each of these. 5x-2y=5 It is in slope-intercept form; the slope is m=-2, the x-intercept is (1,0), and the y-intercept is (0,5). It is in standard form; the slope is m=-2, the x-intercept is (1,0), and the y-intercept is (0, 5/2). It is in standard form; the slope is m=5/2, the x-intercept is (1,0), and the y-intercept is (0,-5/2). It is in point-slope form; the slope is m=5/2, the x-intercept is (1,0), and the y-intercept is (0,-5/2).

Determine which form of a line the given equation is in. Then, determine the slope, the x-intercept, and the y-intercept. Select the answer choice that correctly identifies each of these. 5x-2y=5
It is in slope-intercept form; the slope is m=-2, the x-intercept is (1,0), and the y-intercept is (0,5).
It is in standard form; the slope is m=-2, the x-intercept is (1,0), and the y-intercept is (0, 5/2).
It is in standard form; the slope is m=5/2, the x-intercept is (1,0), and the y-intercept is (0,-5/2).
It is in point-slope form; the slope is m=5/2, the x-intercept is (1,0), and the y-intercept is (0,-5/2).

Transcript text: Determine which form of a line the given equation is in. Then, determine the slope, the $x$-intercept, and the $y$-intercept. Select the answer choice that correctly identifies each of these. $5 x-2 y=5$ It is in slope-intercept form; the slope is $m=-2$, the $x$-intercept is $(1,0)$, and the $y$-intercept is $(0,5)$. It is in standard form; the slope is $m=-2$, the $x$-intercept is $(1,0)$, and the $y$-intercept is $\left(0, \frac{5}{2}\right)$. It is in standard form; the slope is $m=\frac{5}{2}$, the $x$-intercept is $(1,0)$, and the $y$-intercept is $\left(0,-\frac{5}{2}\right)$. It is in point-slope form; the slope is $m=\frac{5}{2}$, the $x$ - intercept is $(1,0)$, and the $y$-intercept is $\left(0,-\frac{5}{2}\right)$.

Solution

Solution Steps

To determine the form of the given line equation $5x - 2y = 5$, we first need to identify its structure. The equation is in standard form $Ax + By = C$. To find the slope, $x$-intercept, and $y$-intercept, we can rearrange the equation into slope-intercept form $y = mx + b$ and solve for these values.

Step 1: Identify the Form of the Equation

The given equation is $5x - 2y = 5$. This equation is in the standard form $Ax + By = C$, where $A = 5$, $B = -2$, and $C = 5$.

Step 2: Convert to Slope-Intercept Form

To find the slope and intercepts, we convert the equation to the slope-intercept form $y = mx + b$. Solving for $y$, we get: \[ y = \frac{5}{2}x - \frac{5}{2} \]

Step 3: Determine the Slope

The slope $m$ of the line is the coefficient of $x$ in the slope-intercept form. Thus, the slope is: \[ m = \frac{5}{2} \]

Step 4: Calculate the $y$-Intercept

The $y$-intercept is the constant term in the slope-intercept form, which is the value of $y$ when $x = 0$. Therefore, the $y$-intercept is: \[ (0, -\frac{5}{2}) \]

Step 5: Calculate the $x$-Intercept

The $x$-intercept is the value of $x$ when $y = 0$. Substituting $y = 0$ into the original equation $5x - 2y = 5$, we solve for $x$: \[ 5x = 5 \implies x = 1 \] Thus, the $x$-intercept is: \[ (1, 0) \]

Final Answer

$\boxed{\text{It is in standard form; the slope is } m=\frac{5}{2}, \text{ the } x\text{-intercept is } (1,0), \text{ and the } y\text{-intercept is } \left(0,-\frac{5}{2}\right).}$

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