Substitute \(x = -\frac{4}{5}\) into \(y = 2x + 3\):
["Substitute (x = -\frac{4}{5}) into the Linear Equation (y = 2x + 3): A Step-by-Step Guide", "Linear equations are fundamental in algebra and widely used in science, engineering, and economics. One common task is substituting specific values of (x) to find the corresponding (y). In this article, we explore how to properly substitute (x = -\frac{4}{5}) into the equation (y = 2x + 3), demonstrating the method clearly and accurately.", "### Understanding the Equation", "The given equation is a simple linear function:\n[\ny = 2x + 3\n]\nHere, (y) depends directly on (x), multiplied by a slope of 2, and shifted vertically by 3 units. Substituting any real number for (x) allows us to compute the exact value of (y).", "### Step-by-Step Substitution", "We are substituting:\n[\nx = -\frac{4}{5}\n]", "Substitute (x) into the formula:\n[\ny = 2\left(-\frac{4}{5}\right) + 3\n]", "Perform the multiplication first:\n[\ny = -\frac{8}{5} + 3\n]", "Now convert 3 into a fraction with denominator 5 to combine terms:\n[\ny = -\frac{8}{5} + \frac{15}{5}\n]", "Add the fractions:\n[\ny = \frac{7}{5}\n]", "### Final Result", "So, when (x = -\frac{4}{5}), the corresponding (y) value is:\n[\ny = \frac{7}{5}\n]", "This result can be expressed as a decimal ((1.4)) for practical applications, but the exact fractional form is preferred in algebraic contexts.", "### Why This Substitution Matters", "- Accuracy in Calculations: Proper substitution ensures correct evaluations, especially when teaching or applying linear models.\n- Understanding Functions: This exercise reinforces how variables interact in linear relationships.\n- Foundation for Further Topics: This skill is essential before tackling systems of equations, graphing, or real-world modeling.", "### Summary", "Substituting (x = -\frac{4}{5}) into (y = 2x + 3) yields:\n[\n\boxed{y = \frac{7}{5}}\n]\nThis demonstrates a clear, step-by-step substitution process that strengthens algebraic proficiency and prepares learners for more complex mathematical challenges.", "---", "Keywords: substitute (x = -\frac{4}{5}), linear equation, (y = 2x + 3), algebra problem, function evaluation, exact value, fractional solution."]
